STATISTICS B11

Distribution of English test marks was given as hereunder.

Length(mm)	20 - 27	28- 35	36 - 43	44-51	52 - 59	60 - 67	68 - 75
Frequency	3	5	9	12	6	3	2

Calculate the median.

Solution

Class interval	Frequency(f)	Cumulative frequency
20 - 27	5	5
28- 35	7	12
36 - 43	10	22
44 - 51	12	34
52 - 59	8	42
60 - 67	5	47
68 - 75	3	50
	∑f = 50

N = 45, N/2=22.5, Median class must fall in the cumulative frequency of 25. This has to be 44 – 51.

n_b = 22, n_w = 12, Upper boundary(U)= 51.5, Lower boundary(L) =43.5

i = Upper boundary – Lower boundary

i = 51.5 – 43.5

i = 8

Median = L + (N/2 – n_b)i/n_w

                              

Median = 43.5 + (50/2 – 22)8

                                  12

Median = 43.5 + (25 – 22)8

                                 12

Median = 43.5 + (3)8

                             12

Median = 43.5 + 24

                           12

Median = 43.5 +  2

                               

Median = 43.5

Hence the median is 43.5